Advanced Radio Frequency Identification Design and Applications Part 6 potx

89 Design of a Very Small Antenna for Metal-Proximity Applications δ [μm] The δ values are shown in Fig 3.12 Here, a copper wire is considered, and the σ value is set to 5.8 × 107 [1/Ωm] The t value should be more than four times the δ value The calculated results, i.e., the results obtained using Eq (3.19), are shown in Fig 3.13; an important point to be noted is that the values of Rl are not sufficiently small By substituting the L0 value determined from Fig 3.3 in Eq (3.19), we can calculate the Rl values for NMHAs In Fig 3.3, L0 is about 0.48 m (0.95 × 0.5) at 315 MHz, and hence, Rl is approximately 0.7 Ω If the frequency changes and L and d are changed analogously, Rl becomes inversely proportional to √λ The most effective way to reduce Rl is to increase W or d 0.1 Frequency [GHz] 10 Fig 3.12 Skin depth (δ) 10 W =1 mm Rl [Ω] L =1000 mm L =500 mm L =100 mm 0.1 0.1 Fig 3.13 Ohmic resistance f [GHz] 10 90 Advanced Radio Frequency Identification Design and Applications 3.2.5 Input resistances The simulated input resistances (Rin) of the self-resonant structures are shown in Fig 3.14 Here, Rin is expressed as follows: Rin = Rr+ Rl =RrD + RrL + Rl (3.20) For an Rl value of approximately 0.7 Ω, Rl.shares the dominant part of Rin at H = 0.02 m in Fig 3.14 In these small antennas, most of the input power is dissipated as ohmic resistance, and only a small component of the input power is used for radiation 0.035 4.50 2.21 N= 2.32 N = 10 4.68 2.44 N = 15 4.81 0.030 D [m] 0.025 0.84 0.020 0.015 0.010 0.005 0.92 1.00 R [Ω] 0.02 0.04 0.06 0.08 0.10 H [m] Fig 3.14 Input resistances Table 3.2 gives the details of the input resistances The calculated results, i.e., the results obtained using Eqs (3.2), (3.4), and (3.17), are compared with the simulated results The RrD+RrL values determined from the aforementioned equations agree well with the simulated results The calculated and simulated Rl values also agree well with each other; in the equation, an α value of 0.6 is used Finally, the Rin values are compared, and the antenna efficiencies (η = (RrD+RrL )/Rin) are obtained The calculated and simulated results agree well, and thus, the equations are confirmed to be accurate Moreover, Rl has a large negative effect on the antenna efficiency Structure N=5 H = 0.02λ N = 15 H = 0.02λ RrD[Ω] Eq Sim Eq Sim RrL[Ω] Rl[Ω] Rin[Ω] η[dB] 0.0790 0.2378 0.6380 0.9548 -4.7911 0.5862 0.8399 -5.1988 0.8008 0.9453 -8.1554 0.7988 0.9975 -7.0067 0.2537 0.0790 0.1987 0.0656 Table 3.2 Resistances determined by calculation and simulation 91 Design of a Very Small Antenna for Metal-Proximity Applications 3.2.6 Q factor The Q factor is important for estimating the antenna bandwidth The radiation Q factor (QR) for electrically small antennas is defined as QR = stored energy (Esto)/radiating energy (Edis) (3.21) For antennas, these energies are expressed by the input impedance: Esto = X I2 (3.22) Edis = Rr (3.23) Therefore, Qimp can be expressed as follows: Qimp = X/Rr (3.24) Another expression for the Q factor is based on the frequency characteristics; in this case, the Q factor is referred to as QA: QA = fc/Δf (3.25) Here, fc is the center frequency and Δf is the bandwidth In this expression, a small QA value indicates a large bandwidth McLean [13] gave the lower bound for the Q factor (QM): QM = 1 + ka ( ka)3 (3.26) Figure 3.15 shows examples of QA and QM for NMHAs; Ds is the diameter of the sphere enclosing an NMHA The antenna structures labeled A and B are those shown in Fig 3.16 The QA values of A and B are based on the measured voltage standing wave ratio (VSWR) characteristics shown in Fig 3.19 We can see that QA is smaller than QM, because of the ohmic resistance of the antenna 10000 QM Q A QA B 1000 A 0.015 0.020 0.025 A/ DA/λλ Fig 3.15 Q factors for NMHA 0.030 0.035 92 Advanced Radio Frequency Identification Design and Applications 3.3 Achieving a high antenna gain The efficiency (η) of a small antenna is defined as η = (RrD + RrL)/(RrD + RrL +Rl ) (3.27) Since (see Table 3.2) Rl is greater than Rr (=RrD + RrL,), Rl must be decreased in order to achieve high antenna efficiency From Eq (3.19), it is clear that increasing the antenna wire width (W) or diameter (d) is the most effective way to reduce Rl If W is increased, it would be necessary to ensure that neighboring wires are well separated from each other By substituting Eqs (3.2), (3.4), and (3.19) in Eq (3.27), we can calculate η; the result is shown in Fig 3.16 It can be seen that η decreases with a decrease in H and D In this case, we use a very narrow antenna wire (d = 0.05 mm) At points A and B, η is 10% (-10 dB) and 25% (-6 dB), respectively The relationship between the antenna gain (GA) and η is given by GA = GD η [dBi] (3.28) Here, GD is the directional gain of the antenna In electrically small antennas, GD remains almost constant at 1.8 dBi The antenna gains at points B and A are GA = -4.2 dBi and -8.2 dBi, respectively Given the small antenna size, these gains are large Moreover, the gains can be increased if a thicker wire is used In conclusion, it is possible to achieve a high gain when using small antennas 0.030 η = 40% N=5 0.025 η = 30% η = 20% DA/λ 0.020 0.015 A N=7 B N=11 η = 10% 0.010 d = 0.55 mm 0.005 0.005 0.010 0.015 0.020 HA/λ 0.025 0.030 Fig 3.16 Efficiency of NMHA 3.4 Examples of electrical performance In order to investigate the realistic characteristics, we fabricated a 0.02λ antenna (point B in Fig 3.16), as shown in Fig 3.17 The antenna impedances are measured with and without a 93 Design of a Very Small Antenna for Metal-Proximity Applications tap feed The tap structure is designed according to the procedure given in Section 4.2.4 Excitation is achieved with the help of a coaxial cable The coaxial cable is covered with a Sperrtopf balun to suppress the leak current The measured and calculated impedances are shown in Fig 3.18 The results agree well both with and without the tap feed, thereby confirming that the measurement method is accurate The tap feed helps in bringing about an effective increase in the antenna input resistance The bandwidth characteristics are shown in Fig 3.19; the measured and simulated results agree well The bandwidth at VSWR < is estimated to be 0.095% 20.0 mm Tap 38.0 mm 16.0 mm 19.3 mm (a) w/o tap Sperrtopf balun (a) With tap Fig 3.17 Fabricated antenna (H = 0.021λ, D = 0.020λ) 50j 25j 100j 250j 10j With tap w/o tap 10 -10j 25 50 100 250 315 MHz -250j Simu Meas -25j -100j -50j Fig 3.18 Antenna input impedance 94 Advanced Radio Frequency Identification Design and Applications 3.0 VSWR 2.5 0.30 MHz 2.0 0.30 MHz 1.5 Simu Meas 1.0 314.6 314.8 315.0 315.2 Frequency [MHz] 315.4 Fig 3.19 VSWR characteristics Sim Eθ =-5.6 dBi Eφ = -8.5120 dBi Meas 90 -5 Eθ =-5.3 dBi Eφ60 -8.2 dBi = -10 -15 150 30 -20 -25 -30 180 -25 -20 210 330 -15 -10 240 -5 270 300 Fig 3.20 Radiation patterns As can be seen from Fig 3.20, the measured and simulated radiation characteristics are in good agreement The Eθ component corresponds to the radiation from the electric current 95 Design of a Very Small Antenna for Metal-Proximity Applications source shown in Fig 3.1, and the Eφ component corresponds to the radiation from the magnetic current source shown in Fig 3.1 There is a 90° phase difference between the Eθ and Eφ components Therefore, the radiated electric field is elliptically polarized Because the magnitude difference between the Eθ and Eφ components is only dB, the radiation field is approximately circularly polarized The magnitude of the Eθ and Eφ components correspond to RrD in Eq (3.2) and RrL in Eq (3.4) The antenna gains of the Eθ and Eφ components can be estimated by the η value shown in Fig 3.16 The value η × GD (GD indicates the directional gain of 1.5) of structure B becomes -4 dBi This value agrees well with the total power of the Eθ and Eφ components NMHA impedance-matching methods 4.1 Comparison of impedance-matching methods For the self-resonant structures of very small NMHAs, effective impedance-matching methods are necessary because the input resistances are small There are three well-known impedance-matching methods: the circuit method, the displaced feed method, and the tap feed method as shown in Fig 4.1 In the circuit method, an additional electrical circuit composed of capacitive and inductive circuit elements is used In the displaced feed method, an off-center feed is used The amplitude of the resonant current (Idis) is lower at the offcenter point than at the center point (IM), and hence, the input impedance given by Zin = V/Idis is increased As the feed point approaches the end of the antenna, the input resistance approaches infinity This method is useful only for objects with pure resistance Since the RFID chip impedance has a reactance component, this method is not applicable to RFID systems In the tap feed method, an additional wire structure is used By appropriate choice of the width and length of the wire, we can achieve the desired step-up ratio for the input resistance Moreover, the loop configuration can help produce an inductance component, and therefore, conjugate matching for the RFID chip is possible This feed is applicable to various impedance objects (a) Circuit method (b) Displaced feed (c) Tap feed Fig 4.1 Configurations of impedance matching methods The features of the three methods are summarized in Table 4.1 For the circuit method, the capacitive and inductive elements are commercialized as small circuit units These units have appreciable ohmic resistances 96 Advanced Radio Frequency Identification Design and Applications If the NMHA input resistances are around Ω, the ohmic resistance values become significant This method is not suitable for small antennas with small input resistances For the displaced feed method, the matching object must have pure resistance The tap feed method can be applied to any impedance object, but it is not clear how the tap parameters can be determined when using this method Method Advantages Disadvantages Design Circuit method [8] With capacitance and inductance chips, matching is easily achieved Severe reduction in antenna gain by chip losses Theoretical method has been established Displaced feed [9] Simple method of shifting a feed point No reduction in antenna gain Limited to pure resistance objects Displacement position is easily found empirically Tap feed [10] Uses additional structure No reduction in antenna gain Applicable to any object Additional structure increases antenna volume Design method has not been established Table 4.1 Comparison of impedance-matching methods 4.2 Design of tap feed structure [14] 4.2.1 Derivation of equation for input impedance The tap feed method has been used for the impedance matching of a small loop antenna [15] The tap is designed using the equivalent electric circuit The tap configuration for the NMHA is shown in Fig 4.2 The antenna parameters D and H are selected such that selfresonance occurs at 315 MHz The tap is attached across the center of the NMHA, and the tap width and tap length are denoted as a and b, respectively The equivalent electric circuit is shown in Fig 4.3 Here, L, C, and R are the inductance, capacitance, and input resistance, respectively The tap is excited by the application of a voltage V; MA is the mutual inductance between the NMHA and the tap In the network circuit shown in Fig 4.3, the circuit equations for the NMHA and the tap are as follows: ⎧ ⎪ ⎨ ⎪ ⎩ + R+ jω(L− M )⎫ I + jω M (I − I ) = ⎪ A ⎬ A A A T ⎪ jωC ⎭ jω(LT − MA )IT + jω MA(IT − IA) =V (4.1) (4.2) From the above equations, the input impedance (Zin = V/IT) of the NMHA can be deduced: 97 Design of a Very Small Antenna for Metal-Proximity Applications 2 Zin = R(ω MA) R + (ωL − ) ωC +j R (ωLT ) − (ω MA) (ωL − ωC R + (ωL − ) + ωLT (ωL − ) ωC ωC )2 (4.3) Here, the tap inductance (LT) is given by [16]: LT = ⎤ μ⎡ ab ab ⎢b ln( ) + a ln( ) + 2( d / + a + b − b − a)⎥ 2 2 π⎢ ⎥ d(b + a + b ) d( a + a + b ) ⎣ (4.4) ⎦ DA d b ~ HA a N Fig 4.2 Tap configuration for NMHA RA V~ IT Tap CA LA IA LT NMHA MA Fig 4.3 Equivalent circuit for tap feed 4.2.2 Simple equation for step-up ratio At the self-resonant frequency (ωr = 2πfr), the imaginary part of Eq (4.3) becomes zero Therefore, we have R (ωr LT ) − (ωr M A )2 (ωr L − ωrC ) + (ωr L − ωr C )2 = (4.5) If the variable of the above equation is replaced by (ωr L – 1/ ωrC) = α, this expression becomes second-order in α The two solutions are 98 Advanced Radio Frequency Identification Design and Applications α (±) = ωr M A2 ± ωr M A − R LT 2 LT (4.6) We label these two solutions α(+) and α(-) For these α values, the resonant points are shown in Fig 4.4 Rin:α(+) Rin:α(-) Fig 4.4 Resonant points In the root of Eq (4.6), the following assumption is applicable This assumption is valid when the tap width (a) is nearly equal to the antenna diameter (D): ωr M A 〉〉 R LT (4.7) Then, the expression for α becomes simple: α (+) = ωr M A LT (4.8) By using α(+) in Eq (4.3), we can derive an expression for the input resistance (Rin): Rin = R( LT / M A )2 (4.9) Finally, the step-up ratio (γ) of the input resistance can be simply expressed as γ = ( LT / M A ) (4.10) The important point to be noted in this equation is that MA has a strong effect on the step-up ratio In the following section, the calculation method and MA results are presented 4.2.3 Calculation method and results for mutual inductance The calculation structure is shown in Fig 4.5 BA is the magnetic flux density in the NMHA, and IT is the tap current MA can be calculated using the following equation [17]: 99 Design of a Very Small Antenna for Metal-Proximity Applications DA Bi Tap feed IT HA Bi Bj B0 ～a BA b NMHA Bj Fig 4.5 Calculation structure MA = ∫ BA ⋅ dS S IT = μ ∫ H A ⋅ dS (4.11) S IT Here, BA is the sum of the Bi values of each loop in Fig 4.5 The magnetic field (Hi) in each loop is given by H0i = ∫ l IT sin θ dl 4π r (4.12) Here, r represents the distance between a point on the tap and a point inside a loop In this calculation, a current IT exists at the center of the tap wire Therefore, even if the the magnetic field is applied at point close to the tap wire D f=315 MHz d=0.55 mm N=5 0.020 B N=7 0.014 A C 0.005 Fig 4.6 Study structures of NMHA 0.021 N=11 E 100 Advanced Radio Frequency Identification Design and Applications To establish the design of the tap feed, the LT/MA values in Eq (4.10) must be represented by the structural parameters Calculations are performed for the structures shown in Fig 4.6 Points A, B, and C are used to investigate the dependence of MA on the structural parameters 0.4 0.5 0.6 1.5 Eq (4.11) 2.0 (MA/L0 )B 0.15 0.19 0.23 b/D A 1.5 2.0 (MA/L0 )A b/D A b/D A 2.0 1.5 (MA/L0 )C 0.16 0.20 0.24 Eq (4.11) A structure×0.34 1.0 0.5 0.6 0.7 0.8 0.9 1.0 a/DA Eq (4.11) A structure×0.37 1.0 0.5 0.6 0.7 0.8 0.9 1.0 a/DA 1.0 0.5 0.6 0.7 0.8 0.9 1.0 a/DA Fig 4.7 Calculated results: MA/L0 The calculated MA values are shown in Figs 4.7(a), (b), and (c) The MA value is normalized by the L0 value, which is the self-inductance of a small loop with diameter D L0 is given by [18] L0 = μD ⎧ 8D ⎫ ⎨ln( ) − 1.75 ⎬ ⎩ d ⎭ (4.13) Structure A in Fig 4.7(a) is used as a reference to determine the dependence of MA on the structural parameters Comparison of structures A and B reveals the dependence of MA/L0 on HA and DA Taking into account Eq (4.11), we show that MA is proportional to DA/HA The DA/HA value for structure B becomes 0.34 times that for structure A In Fig 4.7(b), the solid lines indicate the calculated results obtained using Eq (4.11) The dotted lines indicate the transformed values, i.e., the product of the values in Fig 4.7(a) and 0.34 The data corresponding to the solid and dotted lines are in good agreement, thus confirming that the MA/L0 values are proportional to the DA/HA value We now compare structures A and C Eq (4.11) shows that MA is proportional to N/HA The N/HA value for structure C is 0.37 times that for structure A In Fig 4.7(c), the solid lines indicate the calculated results obtained using Eq (4.11) The dotted lines indicate the transformed values, i.e., the product of the values shown in Fig 4.7(a) and 0.37 The solid and dotted lines agree well, confirming the proportional relationship between MA/L0 and N/HA value We thus have Design of a Very Small Antenna for Metal-Proximity Applications M A DA N ∝ L0 HA 101 (4.14) 4.2.4 Universal expression for MA The design equation becomes universal if the MA/L0 value is expressed in terms of M0/L0 Here, M0 is the mutual inductance between the one-turn loop and a tap If we introduce a coefficient αA, MA/L0 can be given by MA D N M0 = αA A L0 H A L0 (4.15) The M0/L0 values calculated using from Eq (4.11) (assuming N = 1) are shown in Fig 4.8 The M0/L0 values show small deviations with the DA values If all the structural deviations depending on DA, HA, and N are contained in the coefficient term, αA can be expressed as follows: α = 0.05 + 0.0075N + 4.5( H ) N 2D We use DA = 0.020λ (see Fig 4.8) for the M0/L0 values M0 /L0 0.12 0.17 DA=0.014λ D A=0.020λ DA=0.029λ Fig 4.8 Calculated results: M0/L0 4.2.5 Design equation for step-up ratio in NMHA tap feed By applying Eq (4.15) to Eq (4.10), we can express the step-up ratio (γ) as follows: (4.16) 102 Advanced Radio Frequency Identification Design and Applications γ =( LT H A LT HA ) =( ) ( ) =( ) γ0 α ADA N M0 α ADA N MA (4.17) This equation is the objective design equation for a tap feed Here, γ0 is given by γ0 = ( LT ) M0 (4.18) The calculated γ0 values are shown in Fig 4.9 For each γ0, the tap structural parameters a/DA and b/DA are given γ0=(LT/M0)2 120 DA=0.014λ D A=0.020λ DA=0.029λ 80 40 Fig 4.9 Calculated results: γ0 4.2.6 Design procedure for tap feed We now summarize the design procedure First, the self-resonant NMHA structure is determined on the basis of Fig 3.2 or Eq (3.16) Then, the antenna input resistance is estimated using Eqs (3.2), (3.4), and (3.19) The requested γ value is determined by taking into account the feeder line impedance Then, Eq (4.17) is used to determine the tap structure The γ0 value is determined by substituting the antenna parameters and γ value in Eq (4.17) The final step involves the use of the data provided in Fig 4.9 The objective γ0 curve in Fig 4.9 is identified Then, the relation between a/DA and b/DA is elucidated, and a suitable combination of a/DA and b/DA is selected Antenna design for RFID tag In this section, the proximity effect of a metal plate on the self-resonant structures and radiation characteristics of the antenna is clarified through simulation and measurement An 103 Design of a Very Small Antenna for Metal-Proximity Applications operating frequency of 953 MHz is selected, and antenna sizes of 0.03λ–0.05λ are considered We discuss the fabrication of tag antennas for Mighty Card Corporation [19] 5.1 Design of low-profile NMHA [20] The projection length of the NMHA is reduced by adopting a rectangular cross section, so that the antenna can be used in an RFID tag The simulation configuration is shown in Fig 5.1 The antenna thickness is T, and the size of the metal plate is M The spacing between the antenna and the metal plate is S The equivalent electric and magnetic currents are I and J, respectively Eθ and Eφ correspond to the radiation from the electric and magnetic currents, respectively z θ I J M L x φ Eθ Eφ y W T M Fig 5.1 Simulation configuration The most important aspect of the antenna design is the self-resonant structure The selfresonant structure without a metal plate is shown in Fig 3.10 The design equation (Eq (3.16)) is not effective when a metal plate is present in the vicinity of the antenna Therefore, the self-resonant structure is determined by electromagnetic simulations The calculated self-resonant structures are shown in Fig 5.2; T and N are variable parameters Other parameters, such as d, S, and M are shown in the figure For small values of T, large W values are required so that the cross-sectional area is maintained at a given value For smaller values of N, too, large W values are required so that the individual inductances of the cross-sectional areas are increased An example of the input impedance in the structure indicated by the triangular mark at T = mm is shown in Fig 5.3 At 953 MHz, the input impedance becomes a pure resistance of 0.49 Ω Because the antenna has a small length of 0.04λ, the input resistance is small The radiation characteristics are shown in Fig 5.4 To simplify the estimation of the radiation level, the input impedance mismatch is ignored by assuming a “no mismatch” condition in the simulator The dominant radiation component is Eφ,, which corresponds to the magnetic current source Surprisingly, an antenna gain of –0.5 dBd is obtained under these conditions Here, the unit dBd represents the antenna gain normalized by that of the 0.5λ dipole antenna The high gain is a result of the appropriate choice of the ohmic resistance (Rl) on 104 Advanced Radio Frequency Identification Design and Applications the basis of the radiation resistance (Rr) Rl is determined from the antenna wire length and d given by Eq (3.19) Here, because Rr is 0.24 Ω, Rl should be smaller than this value To achieve a small ohmic resistance, d should be made as large as possible When d is 0.8 mm, Rl is 0.25 Ω, and hence, a radiation efficiency of about 50% is achieved This antenna gain confirms that a small rectangular NMHA in close proximity to a metal can be used in several practical applications 0.1 0.09 N=4 XL' = XD' Antenna width (W/λ) 0.08 N=5 0.07 N=6 0.06 T=1mm N=4 XL = XD 0.05 N=5 0.04 N=6 0.03 Frequency=953MHz, d=0.8mm Metal plate size：M=1λ, S=1mm 0.02 0.03 M/ λ 965 0.49Ω 953MHz 940 0.04 Antenna length (L/λ) Fig 5.2 Self-resonant structures Fig 5.3 Input impedance T=3mm 0.05 105 Design of a Very Small Antenna for Metal-Proximity Applications Eθ = -20dBd Eφ = -0.5dBd 1mm M E T A L Fig 5.4 Radiation characteristics T=3mm Eφ T=1mm Magnetic current source Electric current source Eθ N=4 N=5 N=6 T=3mm T=1mm M=1 wavelength Fig 5.5 Radiated field components 106 Advanced Radio Frequency Identification Design and Applications The important antenna gain characteristics for the self-resonant structures are shown in Fig 5.5 It is noteworthy that the Eφ components are dominant, while the Eθ components are less than –20 dBd There is no difference in the antenna gain even when N is changed For large T values, a high antenna gain is achieved When T is mm, the gain is expected to be comparable to that of a 0.5λ dipole antenna Moreover, the antenna gain remains constant for different values of L Hence, excellent antenna gains may be obtained for small antenna sizes such as 0.03λ 5.2 Practical antenna characteristics A high gain can be expected for a small NMHA However, because the input resistance of such an antenna is small, an impedance-matching structure is required for practical applications A tap-matching structure is used for a 50-Ω coaxial cable, as shown in Figs 5.6(a) and (b) The tap structure is rather simple Wire diameters of 0.8 mm and 0.5 mm are selected for the antenna and the tap, respectively Because the spacing between the antenna and the metal plate is small (1 mm), appropriate arrangement of the tap arms is important Metal plate Antenna L : 12.6mm (0.04λ) Tap W : 12.3mm (0.039λ) (a) Perspective view F1 :12.3mm T:3mm (0.01 ) F2 :4mm S:1mm d:0.5mm Metal plate (b) Cross-sectional view Fig 5.6 Experimental NMHA structure The fabricated antenna and feed cable are shown in Fig 5.7 The tap arms are soldered to the antenna wire, and a coaxial cable is used as a feed line A Sperrtopf balun is attached to the coaxial cable to suppress leak currents Figure 5.8 shows the measured and calculated antenna impedances The measured and calculated values are in good agreement, both in 107 Design of a Very Small Antenna for Metal-Proximity Applications the presence and absence of the tap feed When the tap feed is used, the antenna impedance is exactly 50 Ω, and this confirms the effectiveness of the tap feed The bandwidth characteristics are shown in Fig 5.9 A 3.5-MHz bandwidth is obtained when VSWR < This bandwidth corresponds to 0.4% of the center frequency Antenna Balun L : 12.6mm (0.04λ) W : 12.3mm (0.039λ) Tap Coaxial cable Fig 5.7 Fabricated NMHA structure Without tap feed 0.49Ω With tap feed 50Ω 953MHz Cal Meas Fig 5.8 Input impedance The important radiation characteristics observed when the antenna is placed near a metal plate are shown in Fig 5.10 The separation S in this case is mm A square metal plate with a size of 0.5λ is used The Eφ component is dominant when the antenna is in close proximity to the metal plate A high antenna gain of –0.5 dBd is achieved The Eφ level in the presence of the metal plate exceeds that in the absence of the metal plate by about 10 dB The usefulness of the NMHA in a metal-proximity application is verified At the same time, the intensity of the Eθ component decreases to –11 dBd This shows that the electrical current source does not work well under metal-proximity conditions 108 Advanced Radio Frequency Identification Design and Applications Fig 5.9 VSWR characteristics Eθ = − 10.1 Eφ = − 0.53dBd Cal.(dotted) Eθ = −10.4 Eφ = −0.53dBd Meas.(solid) Fig 5.10 Radiation characteristics 5.3 RFID tag antenna In order to use the rectangular NMHA as a tag antenna, the input impedance must be matched to the IC impedance of ZIC = 25 – j95 Ω Therefore, the antenna size and tap size are modified as shown in Fig 5.11 The tap length is increased to obtain the necessary inductance for achieving conjugate matching with the IC capacitance The spacing between the antenna and the metal plate is set to 1.5 mm A 0.5λ square metal plate is used The impedance-matching process is shown in Fig 5.12 The tap length (T3) is important for matching the impedance to the IC Almost complete conjugate matching can be achieved at T3 = 17 mm  ... Antenna input impedance 94 Advanced Radio Frequency Identification Design and Applications 3.0 VSWR 2.5 0.30 MHz 2.0 0.30 MHz 1.5 Simu Meas 1.0 314 .6 314.8 315.0 315.2 Frequency [MHz] 315.4 Fig... the capacitive and inductive elements are commercialized as small circuit units These units have appreciable ohmic resistances  96 Advanced Radio Frequency Identification Design and Applications. .. The two solutions are 98 Advanced Radio Frequency Identification Design and Applications α (±) = ωr M A2 ± ωr M A − R LT 2 LT (4 .6) We label these two solutions α(+) and α(-) For these α values,